Major-General Mohammed Jawan Huweidi, commander of the Iraqi Army's 14th division, said: "We have control of the towns around Basra and also inside the city. There are no clashes anywhere in Basra. Now we are dismantling roadside bombs."
An overnight curfew remains in place in Basra but authorities said that schools would reopen on Tuesday.
In Baghdad, the curfew was lifted on Monday morning, although vehicle restrictions remained in place in three predominantly Shia neighbourhoods, including Sadr City.
Families were venturing out to bury their dead.
James Bays, Al Jazeera's correspondent in Baghdad, said that although al-Sadr's fighters seemed to be observing his order, civilians were nervous that the fighting would flare up again.
Haider al-Asadi, a fighter in Sadr City, said all the al-Mahdi Army fighters were "now sitting in their homes".
"But we are ready, should the Americans come inside our district, to fight. We have enough IEDs [improvised explosive devices] for them. If they come, we will defend ourselves."
Asadi said that US troops were still on the edge of the neighbourhood and had deployed snipers on the rooftops of houses.Iraqi political officials, speaking on condition of anonymity, said Iran had played a key role in brokering the peace deal between the Iraq's Shia-led government and al-Sadr.
In response to al-Sadr's order on Sunday, the government agreed not to pursue those involved in the fighting provided they put away their weapons.
Nuri al-Maliki, the Iraqi prime minister who personally supervised the Basra operation, admitted that the crackdown had not been entirely successful.
"We came here [to Basra] to pursue criminal gangs and murderers ... our forces were not ready for this battle and we were surprised," he told al-Iraqiya, a state television service.
The deal with al-Sadr meant that his supporters were able to keep hold of their weapons despite the best efforts of government forces to take control of the city.
However, Major-General Abdul Aziz, Iraqi commander, said that by Sunday security forces had managed to clear five areas of Basra which were known Mahdi Army strongholds - Al-Najibiyah, Al-Makkal, Al-Ashhar, Al-Zubair and Qarmat Ali.
Senior figures in Iraq's major Shia parties and representatives of the Iranian Revolutionary Guard held the negotiations in the Iranian city of Qom, one Iraqi Shia official said.
Jabbar Sabhan, a civil servant in Basra, said he was glad the violence had died down but was doubtful the calm would hold.
"I didn't go to work today. It is true that there are no clashes, gunmen or explosions, but the situation is still dangerous. I don't trust the words of politicians," he said.